Avg DPS - Attack Speed Buffs

From Townstons

Attack Speed is shown on the Character Sheet as a number which represents the number of attacks per second.

On wielded items it is shown as a descriptive term. From slowest to fastest they are:

  • Grandma
  • Slothful
  • Normal
  • Fast
  • Freakin' Fast
  • Ludicrous

The trade off for increased speed however, is less damage per attack. The Min-Max Damage of a Grandma weapon is generally, far higher than the Min-Max Damage of a comparable Ludicrous Weapon.

Essentially, it comes down to sizing the right tool for the right job. Sure it can be very satisfying to swing mightily and crush the walnut into oblivion, but you would probably also destroy the table and the follow through would probably put a big dent in your floor. (Oh yeah!... Tremble before me cowardly walnut! FEEL THE MIGHT OF THOR! Smite that walnut!)

After the 200th walnut however, with sweat pouring down your face and walnut powder all the over the place you'd probably start wishing for a something lighter. Lots of wasted energy and the walnut powder probably isn't useful for anything other than baklava. Get a smaller hammer!

However, there maybe a situation where you don't have to clear out a bunch of fodder and you have one nice Boss with lots of HP. (Oh yeah Abby you can take it!) Just keep in mind, that if you miss; you miss big and it's while before you can swing that big heavy weapon again. Abby will just look at you with a shit-eating grin and proceed to "kung-fu" your ass.

The solution to cracking open piles of walnuts and wiping that grin off of Abby's face, Swing Faster!


Contents

Increasing Attack Speed

Now you want to do your best imitation of "Sport Goofy", except without missing. (See here from about 4:10 to 4:18 and you'll get the idea.)

Increasing the Attack Speed can be achieved in a few ways:

All can be used at the same time and have a cumulative (added together) as opposed to a multiplying effect.


Rounding Errors

Fractional numbers in Dungeon Runners are represented as 8-bit fractions in logic calculations. There is a possibility that the calculations shown may not exactly match what will be displayed on the the Character Sheet.
There is an additional possibility that attack speeds may be (further) rounded due to animation and frame rate considerations.

See: Rounding Errors for more detailed information and sample calculation.


Duty Cycle

Duty cycle is the ratio of ON-Time to Total Cycle Time.

When dealing with Attack Speed Buffs it is important to remember that the Buff is NOT in operation for a significant portion of time. The Avg DPS when buffed can be significantly different from when unbuffed. As a result both buff-on time vs buff-off time should be considered when considering the effect of Buffs on Avg DPS.


Effect of Attack Speed on Avg DPS

Consider the Basic Avg DPS Equation:

Avg DPS = 
  min dmg + max dmg  
2 x attack speed


Attack Speed taking account +%Attack Speed from equipment, Passives and Self Buffs:
(The static speed bonuses from equipment and passives will be lumped together.)

Attack Speed = 
(
Base Attack Speed
( 1 + %spd bonus + %buff bonus )
)
       [5]


Substituting for attack speed, in the Avg DPS equation becomes:

Avg DPS (Speed) = 
  (min dmg + max dmg ) x ( 1 + %spd bonus + %buff bonus ) 
2 x Base Attack Speed

Since the buff bonuses only count when they're in operation:


For Single Weapons:
Avg DPS (Speed) =  (
min dmg + max dmg
2 x Base Attk Spd
) x (
ON x ( 1 + %spd bonus + %buff bonus )
ON + OFF
+
OFF x ( 1 + %spd bonus )
ON + OFF
)    [6A]


The bonus 20% added to weapons that are dual wielded must be accounted for, hence:


For Dual Wielding:
Avg DPS (Speed) =  (
min dmg 1 + max dmg 1 + min dmg 2 + max dmg 2
2 x (Base Attk Spd 1 + Base Attk Spd 2)
) x (
ON x ( 1 + 20% + %spd bonus + %buff bonus )
ON + OFF
+
OFF x ( 1 + 20% + %spd bonus )
ON + OFF
)    [6B]


Example - Single Wield, Avg DPS (Speed)


A naked ranger, wields a weapon:

From their character sheet:
Min Damage = 2000 and Max Damage = 4000
Attack Speed = 0.30 (naked)

Then the ranger

puts Trigger Happy in their skill bar, +25% Ranged Attack Speed
equips a total of +14% Ranged Attack Speed
and is planning to use:
Rank 10 Trigger Finger Frenzy
+115% Ranged Attack speed, 15 second duration, 45 second cool down time.
First, tally up the non-buff +% Ranged Attack Speed Bonuses:
(25% + 14%) = 39%


Second, figure out ON-Time, OFF-Time, ON-OFF Time:
ON = duration = 15
OFF = (Cool Down - ON-Time) = 45-15 = 30
ON+OFF = Cool Down = 45


Plugging in all the values into [6A]:


For Single Weapons:
Avg DPS (Speed) = 
(
2000 + 4000
2 x 0.30
) x (
15 x ( 1 + 39/100 + 115/100 )
45
+
30 x ( 1 + 39/100 )
45
)
 
(
   6000   
2 x 0.30
) x (
15 x ( 1 + 0.39 + 1.15 )
45
+
30 x ( 1 + 0.39 )
45
)
 
(
6000
0.60
) x (
38.1
45
+
41.7
45
)
 
10000 x (0.84667 + 0.92667)
 
Avg DPS (Speed) =  17733.4


The Avg DPS (Speed) = 17733 for this single weapon. This Avg DPS represents the potential Avg DPS that can be achieved with an attack speed bonuses + buff.
In the above example, while the buff is in effect, the DPS peaks at 25400 DPS for 15 seconds. Un-buffed, the DPS is 10390 DPS for at least 30 seconds. Any extra delays beyond the remaining cool down time will get added to the OFF Time and therefore the ON+OFF Time. This will have the effect of bring the Avg DPS closer to the un-buffed value, the longer the delay is.
Don't delay unless you're saving it for one particular monster; say a healer, for instance.


Example - Dual Wield, Avg DPS (Speed)


A naked fighter, wields two weapons:

From their character sheet:
Main Min Damage = 530 and Main Max Damage = 1050
Main Attack Speed = 0.60 (naked)
Offhand Min Damage = 600 and Offhand Max Damage = 990
Offhand Attack Speed = 0.47 (naked)

Then the fighter

puts Way of the Roo in their skill bar, +25% Melee Attack Speed
equips a total of +19% Melee Attack Speed
and is planning to use:
Rank 10 1H Swivel Arm Action
+37% Melee Attack speed, 30 second duration, 80 second cool down time.
First, tally up the non-buff +% Melee Attack Speed Bonuses:
(25% + 19%) = 44%


Second, figure out ON-Time, OFF-Time, ON-OFF Time:
ON = duration = 30
OFF = (Cool Down - ON-Time) = 80-30 = 50
ON+OFF = Cool Down = 80


Plugging in all the values into [6B]:


For Dual Wielding:
Avg DPS (Speed) = 
(
530 + 1050 + 600 + 990
2 x ( 0.60 + 0.47 )
) x (
30 x ( 1 + 20/100 + 44/100 + 37/100 )
80
+
50 x ( 1 + 20/100 + 44/100 )
80
)
 
(
   3170   
2 x 1.07
) x (
30 x ( 1 + 0.20 + 0.44 + 0.37 )
80
+
50 x ( 1 + 0.20 + 0.37 )
80
)
 
(
3170
2.14
) x (
60.3
80
+
78.5
80
)
 
1481.31 x (0.7538 + 0.9813)
 
Avg DPS (Speed) =  2570.2


The Avg DPS (Speed) = 2570 for this dual wield example. This Avg DPS represents the potential Avg DPS that can be achieved with attack speed bonuses + buff.